Lesson 5
Solve Problems with Percent
Name: Prerequisite: Unit Rate
Study the example showing how to find the unit rate.
Then solve problems 1–7.
Example
A bus driver made 100 stops on his route in 5 days. The
double number line shows the relationship between the
number of stops and the number of days.
Stops 0
20
40
60
80
Days 0
1
2
3
4
100 120 140 160
5
6
7
8
In the diagram, 100 and 5 represent the ratio of 100 stops
to 5 days.
You can write a multiplication equation to show how
5 days and 100 stops are related.
5 3 20 5 100
1 Look at the corresponding pairs of numbers on the
number lines. Write a multiplication equation to show
how 3 days and 60 stops are related. Repeat for two
other corresponding pairs of numbers.
2 What is the relationship between the number of stops
and each corresponding number of days?
3 What is the rate of stops per day? What is the unit rate?
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Vocabulary
rate a ratio that
compares the first
quantity to only one of
the second quantity.
unit rate the number in
a rate that is being
compared to 1.
Lesson 5 Solve Problems with Percent
41
Solve.
Use the following situation to solve problems 4–5.
Caroline earns $54 babysitting for 6 hours.
4 Fill in the blanks on the double number line to show
the relationship between the amount of money
Caroline earns and the number of hours she works.
Money ($) 0
Hours 0
36
18
1
3
54
5
63
6
8
5 What is Caroline’s rate, in dollars per hour?
What is her unit rate?
6 Ling uses 21 bananas to make 7 fruit smoothies.
What is the rate that Ling uses for bananas per each
smoothie? What is the unit rate? Explain how to use
equivalent fractions to find the answer.
7 Kelly drove 440 miles in 8 hours. Alberto drove
468 miles in 9 hours. Both drove at a constant speed.
Who drove farther in 1 hour? How many miles farther?
Show your work.
Solution: 42
Lesson 5 Solve Problems with Percent
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Lesson 5
Name: Percent of a Number
Study the example problem showing how to find the
percent of a number. Then solve problems 1–6.
Example
In an after-school sports program, 70% of 400 students
play soccer. How many students play soccer?
You can use a model to find 70% of 400.
40
40
40
40
40
40
40
40
40
40
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
The model shows 400 divided into groups of 40. Each
group of 40 represents 10% of 400, so 7 groups of
40 represent 70% of 400. This means that 70% of 400
is 7 • 40, or 280.
There are 280 students who play soccer.
1 What is 70% written as a fraction? 2 Use the fraction to write and evaluate a multiplication
expression that represents 70% of 400. Compare the
answer to the one you got using the model.
Show your work.
Solution: 3 What is 75% of 400? Write and evaluate an expression
to find the answer. Then explain how to use the model
to justify the answer.
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Lesson 5 Solve Problems with Percent
43
Solve.
Use the following situation to solve problems 4–5.
The results of a survey show that 40% of 300 students
chose conserving natural resources as the top priority for
their generation.
4 How many students chose conserving natural
resources? Make a model to find the answer.
Show your work.
Solution: 5 Suppose only 24% of 300 students chose conserving
natural resources. How many students chose
conserving natural resources? Explain how you found
your answer. How can the model help you justify the
answer?
6 There are 50 puzzles in Maggie’s puzzle book. Maggie
finished 30% of the puzzles. How many puzzles does
she have left to do?
Show your work.
Solution: 44
Lesson 5 Solve Problems with Percent
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Lesson 5
Name: Finding the Whole
Study the example problem showing how to find the
whole when a part and the percent are given. Then solve
problems 1–6.
Example
Carmen saved $27, which was 30% of the money she
earned. How much did Carmen earn?
You can use a double number line to find the whole when
a part and the percent are given.
30% of Carmen’s
earnings.
10% of Carmen’s
earnings.
Money ($) 0
9
Percent 0
10
100% of Carmen’s
earnings.
27
20
30
90
40
50
60
70
80
90
100
Carmen earned $90.
1 How can you find 10% of Carmen’s earnings using the
ratio 27 to 30? What is 10% of Carmen’s earnings?
2 How many times as great as 10% is 100%?
3 How can you find 100% of Carmen’s earnings using
the ratio of her earnings to 10%? What is 100% of
Carmen’s earnings?
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Lesson 5 Solve Problems with Percent
45
Solve.
4 Diane received 300 votes in the election for student
council president. That was 60% of the students who
voted in the election. How many students voted in
the election? Use a double number line in your
explanation.
5 Students sold 80% of the books donated to the used
book sale. They sold 48 books in all. How many books
were donated to the used book sale? Use a table in
your explanation.
6 Omar spends $63 on souvenirs during his vacation.
That is 35% of the money he brought with him.
How much money does Omar have left to spend?
Show your work.
Solution: 46
Lesson 5 Solve Problems with Percent
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Lesson 5
Name: Solve Problems with Percent
Solve the problems.
1 Jamil traveled 210 miles, which is 70% of the total
distance to his grandfather’s house. How many more
miles does he need to travel to reach his grandfather’s
house?
A 90 miles
C 300 miles
B 147 miles
D 390 miles
You need to make
two calculations to
solve this problem.
Kate chose B as the correct answer. How did she get
that answer?
2 Brandon plowed snow from 84 driveways in 7 days.
He plowed the same number of driveways each day.
Tell whether each statement is True or False.
a. The rate is 84 driveways to 1 day.
b. The unit rate for driveways per day is 12.
u True u False
u True u False
c. The rate in fraction form is ​ 12  ​.
u True u False
d. If Brandon continues at the same
rate, he will plow 120 driveways
in 12 days.
u True u False
1
··
3 A meteorologist said that it rained during 20% of the
past 60 days. On how many days did it not rain?
Show your work.
Use the ratio of
driveways to days to
help you.
What operation does
the word “of”
indicate?
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Lesson 5 Solve Problems with Percent
47
Solve.
4 At tryouts for the school talent show, 60% of
How many groups of
3 are in 60%?
30 performers played a musical instrument.
How many performers played a musical instrument?
Use the model to find the answer.
3
3
3
3
3
3
3
3
3
3
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
A 3 performers
C 30 performers
B 18 performers
D 60 performers
5 Students collected 600 cans for the canned food drive.
That was 80% of their goal. How many more cans do
they need to collect to reach their goal?
Show your work.
Do you need to find
the part or the
whole?
Solution: 6 Megan correctly spelled 45 out of 50 words in a
spelling competition. Justin spelled 27 out of
30 words correctly. Fernando spelled 84 out of
120 words correctly. Which statements are true?
Select all that apply.
How can you find
a percent using a
ratio?
A Fernando spelled the greatest percent of
words correctly.
B Megan and Justin spelled the same percent of
words correctly.
C Justin spelled the least percent of words correctly.
D The percent of words that Megan spelled correctly is greater
than the percent of words that Fernando spelled correctly.
48
Lesson 5 Solve Problems with Percent
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